Position determining apparatus

ABSTRACT

An apparatus for precisely locating the position of a transmitter either along a line, or a surface, or within a three dimensional space. More particularly the apparatus of the invention is adapted for use with a computer and includes a pen sized movable transmitter, or mouse, whose exact position can be determined without the use of any physical connection between the transmitter and the balance of the apparatus.

BACKGROUND OF THE INVENTION

This is a Continuation-In-Part of presently copending application Ser.No. 07/292,947 filed 1-3-89 now U.S. Pat. No. 4,885,433.

FIELD OF THE INVENTION

The present invention relates generally to a position determiningapparatus. More particularly, the invention concerns an input device foruse with a computer in which the transmitter of the device, or mouse, isin the configuration of a pen sized writing instrument.

DISCUSSION OF THE PRIOR ART

The conventional prior art mouse comprises an input device, usuallyconnected by a wire or other physical linkage to the computer. The mousetypically has a roller on its bottom designed to roll along the desk topbeside the computer. When the mouse is moved, the cursor on the computerscreen will move in the same direction that the mouse is moved.

The drawbacks of the conventional prior art mouse and of prior artposition determining devices are several. In the first place the shapeof the mouse is ill-suited for use as a writing instrument anddisadvantageously requires some physical connection with the computersystem. Further, the conventional mouse only has the ability todetermine position changes relative to a previous position as opposed tobeing able to determine an absolute position relative to a fixedreference. Additionally, unlike the device of the present invention,many prior art position locating devices must be used with a specialsurface such as a digitizing tablet. Finally prior art position locatingdevices are typically two dimensional and cannot determine positionthree dimensionally.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an apparatus forprecisely locating the position of a transmitter within either a plane,within a three dimensional space, or along a line. More particularly, itis an object of the invention to provide an input apparatus for use witha computer which includes a compact movable transmitter, whose exactposition within a plane, three dimensional space, or along a line can bedetermined without the use of any physical connection between thetransmitter and the rest of the apparatus.

It is another object of the invention to provide apparatus of theaforementioned character in which the transmitter has the shape of awriting instrument such as a pen.

It is another object of the invention to provide a device of thecharacter described in the preceding paragraph in which the absoluteposition of the pen sized transmitter can be precisely determinedrelative to a fixed reference.

Another object of the invention is to provide an apparatus of thecharacter described which does not require the use of any specialwriting surface.

A further object of the invention is to provide an apparatus of theclass described in which the transmitter comprises a laser diode driverand in which the apparatus includes photodiode receivers for receivingsignals from the transmitter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a generally perspective view of the one form of the apparatusof the invention.

FIG. 2 is a generally diagrammatic view illustrating the interactionamong the various subsystems which comprise the apparatus of theinvention.

FIG. 3 is a generally diagrammatic view illustrating the phaserelationship of the transmitter signals at the three receivers of theapparatus with the transmitter in a first location.

FIG. 4 is a diagrammatic view similar to FIG. 3, showing the phaserelationship of the signals at the three receivers with the transmitterin a second location.

FIG. 5 is a generally diagrammatic view similar to FIGS. 3 and 4, butshowing the phase relationship of the signals at the three receiverswith the transmitter in a third location.

FIG. 6 is a generally schematic view of the circuitry of the basictransmitter of one embodiment of the apparatus of the invention.

FIG. 7 is a generally schematic view illustrating the circuitry of thebasic receiver of one embodiment of the apparatus of the invention.

FIG. 8 is a generally schematic view showing the circuitry of basicphase detector of one form of the apparatus of the invention.

FIG. 9 is a generally perspective view of an alternate embodiment of theapparatus of the invention.

FIG. 10 is a generally diagrammatic view illustrating an alternatemethod of operation of the apparatus of the invention.

FIG. 11 is a generally schematic view of one form of the phase detectordevice of the apparatus of the invention.

FIG. 12 is a generally diagrammatic view illustrating the interactionamong certain of the various subsystems which comprise an alternateembodiment of the invention.

FIG. 13 is a generally diagrammatic view illustrating the interactionamong certain of the subsystems which comprise yet another form of theinvention.

FIG. 14 is a generally diagrammatic view illustrating the interactionamong certain of the subsystems which comprise still another alternateembodiment of the invention.

DESCRIPTION OF THE INVENTION

Referring to the drawings and particularly to FIGS. 1 and 2, one form ofposition determining apparatus of the present invention is there shown.In this embodiment of the invention the apparatus comprises transmittingmeans for transmitting a detectable signal and three coplanar, spacedapart receiving means for receiving the signal transmitted by thetransmitting means. The transmitting means is here shown as comprising ahousing 12 having the general configuration of a writing pen withinwhich is mounted a laser diode adapted to emit a series of flashes oflight. The receiving means, in turn, comprises first second and thirdreceivers 14, 16, and 18 respectively, each being capable of sensing theflashes of light emitted by the laser diode. Upon sensing the flashes oflight, each receiver generates and transmits corresponding first outputsignals as, for example, electrical signals.

As best seen in FIG. 2, the apparatus further includes first and seconddetector means here provided in the form of first and second phasedetectors 20 and 22. Phase detector 20 is adapted to receive firstoutput signals S1 and S2 from receivers 14 and 16 while phase detector22 is adapted to receive first output signals S2 and S3 from receivers16 and 18. Upon receiving signals S1 and S2 from receivers 14 and 16respectively, phase detector 20 generates and transmits a second outputsignal Vφ1. Similarly, upon receiving signals S2 and S3 from receivers16 and 18 respectively, phase detector 22 generates and transmits athird output signal Vφ2.

Cooperatively associated with phase detectors 20 and 22 is computationmeans shown here as a position computation device 24, for receiving andanalyzing the second and third output signals transmitted by the phasedetectors. The function and operation of the detector and computationmeans will be described more fully in the paragraphs which follow.

Referring now particularly to FIG. 2, with the transmitter positioned asshown by the solid lines, the device functions as follows:

Consider first the receivers 14 and 16, that is, the receivers, numbered1 and 2. In the position indicated by the solid lines and the numeral12, the transmitter is equidistant from receivers 1 and 2. Turning toFIG. 3, the signals detected by receivers 1 and 2, that is, S1 and S2respectively, will be in phase with each other, and phase detector 1will generate the appropriate second output signal, Vφ1.

From the signal Vφ1 it can be readily determined that the transmittermeans must lie somewhere on a line which is equidistant from receivers 1and 2. The line is shown in FIG. 2 as the perpendicular bisector betweenreceivers 1 and 2. The exact position of the transmitter means alongthis line can be determined from the signals available from receivers 2and 3.

With the transmitter in the position shown by the solid lines, it isobviously closer to receiver 2 than it is to receiver 3. Accordingly, byreferring again to FIG. 3 it can be seen that the signal detected byreceiver 2 will lead the signal S3 detected by receiver 3 and phasedetector 2 will generate the appropriate third signal, Vφ2.

From Vφ2 it can be determined that the transmitter must lie on a linesuch that the distance from any point on the line to receiver 2 and thedistance from the same point on the line to receiver 3 are different byan amount (a constant) that results in a phase difference, d1, asindicated in FIG. 3. This line is a hyperbola, designated in thedrawings by the numeral 26, whose equation is determined uniquely by thephase difference d1 as indicated by the third signal Vφ2 and thedistance between receivers 2 and 3.

Having signals Vφ1 and Vφ2 available, the position of the transmitterwithin the plane defined by receivers 1, 2, and 3 can be readilydetermined. To recapitulate, with the transmitter in the position shownby the solid lines in FIG. 2, second signal Vφ1 indicates that thetransmitter lies on the perpendicular bisector between receivers 1 and2. Further, third signal Vφ2 indicates that the transmitter lies on thehyperbola 26 determined by the phase difference d1 and the distancebetween receivers 2 and 3. Since the transmitter lies on both thehyperbola 26 and the perpendicular bisector, the transmitter must be atthe intersection of the hyperbola and the bisector as illustrated inFIG. 2.

The actual computation of the transmitter's position is carried out bythe computation device 24. This device has as its input signals Vφ1 andVφ2 from which the transmitter's position is determined.

If the transmitter's position is altered to that shown by the phantomlines 12a in FIG. 2, it is still equidistant from receivers 1 and 2, butit is further away from the receivers. With the transmitter in thissecond position 12a, the operation of the apparatus is as follows:

Referring particularly to FIG. 4, signals S1 and S2 are still in phasesince the transmitter remains on the perpendicular bisector betweenreceivers 1 and 2. The signal from phase detector 1, that is, secondsignal Vφ1, still indicates this condition. However, as depicted in FIG.4, signal S2 still leads signal S3 as before since the transmitter isstill closer to receiver 2 than to receiver 3. However, the phasedifference d2 is now smaller than d1 since the distances from thetransmitter to receivers 2 and 3 is more nearly equal. In FIG. 4, thethird signal Vφ2, as determined by phase detector 2, reflects thischange.

As before, having signals Vφ1 and Vφ2, the position of the transmittercan readily be determined. Signal Vφ1 again indicates that thetransmitter is located on the perpendicular bisector between receivers 1and 2, and signal Vφ2 indicates that the transmitter lies on a hyperbola28 determined by signal Vφ2 and the distance between receivers 2 and 3.Since Vφ2 has changed, the hyperbola on which the transmitter lies hasalso changed. As before, since the transmitter lies on both the bisectorand the hyperbola 28, it must be located at the point where the bisectorand hyperbola 28 intersect. This position is readily calculated by theposition computation means 24 using signals Vφ1 and Vφ2.

As a further illustration of the operation of this form of positiondetermination apparatus, assume movement of the transmitter to theposition 12b as indicated by the phantom lines designated as 12b in FIG.2. The operation of the apparatus is now as follows:

The location of the transmitter is such that it is closer to receiver 2than it is to receiver 1. This results in signal S2 leading S1, orequivalently, S1 is delayed with respect to S2. This condition isillustrated in FIG. 5. Correspondingly, signal Vφ2 now indicates that S2leads S3 by the amount d4.

With the transmitter in the location 12b, it no longer lies on aperpendicular bisector and a given hyperbola, but rather lies on twohyperbola. One hyperbola 30 is uniquely determined by Vφ1 and thedistance between receivers 1 and 2, and the second hyperbola 32 isuniquely determined by Vφ2 and the distance between receivers 2 and 3.

For the reasons previously discussed, the transmitter must lie on eachof two different hyperbola and more particularly must lie at thelocation 12b where the two hyperbola 30 and 32 intersect.

It should be noted that in the simplified operation of the apparatusjust described, information regarding the phase relationship betweensignals S1 and S3 was not used. In a minimal realization, thisinformation is not necessary. However, if desired, this extrainformation could be used to improve the accuracy of the apparatus. Sucha scheme would be useful in rejecting "noise" and making the apparatusgenerally more precise.

Turning now to FIG. 6 there is illustrated a simple embodiment of thelaser diode driver used in the transmitter of the instant form of theapparatus of the invention. The laser diode illustrated in this figurefunctions to emit the transmitted first, or light flash, signaldescribed in the preceding paragraphs. The laser diode driver isresponsible for applying the necessary power to the laser diode at afrequency dictated by the input oscillator. The circuitry shown in FIG.6 is of a character well known to those skilled in the art and thedetails thereof will not be further described herein.

Referring to FIG. 7, a simple receiver circuit is there illustrated. Thesignal from the transmitter is received by the photodiode detector. Thedetected signal is then passed to the phase detector in a manner wellunderstood by those skilled in the art.

In FIG. 8 a simple phase detector arrangement is shown. The first stageof the phase detector is a set-reset flip-flop whose inputs are drivenby signals from two receivers. Due to the nature of set-resetflip-flops, if the two received signals are exactly in phase, the outputof the flip-flop, "Q", is always low. If the two signals are π radians(180 degrees) out of phase, the output of the flip-flop is a 50% dutycycle square wave. If the two signals are 2 π radians (360 degrees) outof phase, the output of the flip-flop will always be high. In thisfashion, the duty cycle of the flip-flop output varies linearly with thephase difference between the two input signals.

FIG. 8 also shows a low-pass filter following the output of theflip-flop. This filter has a cutoff frequency that is below thefrequency of the input signals. Thus the filter allows only the DC andlow-frequency components of the flip-flop output to pass. If theflip-flop output is a 50% duty cycle square wave, the output of thelow-pass filter will be a voltage that is 50% of the square wave peakvoltage. The plot of output voltage versus phase angle shows how theoutput of the phase detector rises linearly as the phase angle betweenthe two input signals increases. Once again the construction andoperation of the phase detector subassembly illustrated in FIG. 8 iswell understood by those skilled in the art.

Before discussing alternate forms of the present invention, it is to beunderstood that the subsystems of the apparatus, that is the transmittermeans, the receiver means, the detector means and the computation meanscan take several forms. The precise forms of the aforementioned means,as described in the preceding paragraphs and as illustrated in thedrawings, are meant to be exemplary only. For example, the transmittermeans can be such as to transmit various types of signals such as anyelectro-magnetic or acoustic radiation and any sort of modulation as,for example, frequency, amplitude, pulse width, phase and the like.Similarly the receiver means can take numerous forms adapted to receivethe various types of signals that may be transmitted by the transmittermeans. Additionally, the detector and computation means can take variousforms of a character well understood by those skilled in the art, theirprecise form depending upon the end application of the apparatus of theinvention.

Turning to FIG. 10 an alternate approach for transmitter positiondetermination with a plane is there schematically illustrated. Thelocations and configurations of the receivers, transmitter, and phasedetector are substantially the same as described previously. However,analog-to-digital (A/D) converters have been shown for the purposes ofexplanation, but are not essential to the basic invention. Each of theA/D converters 36 and 38 has as its input the output of a phase detectorhereshown as phase detectors 1 and 2. In such a configuration, theoutput of the A/D converter is a digital word that is equal (within aknown constant multiplier) to the phase difference between the inputsignals to the phase detector. The digital word is also equal (within aknown constant multiplier) to the difference between the distances fromthe transmitter to one receiver and from the transmitter to the otherreceiver.

The transmitter coordinates X and Y are the two unknown variables whichare to be determined. Referring to FIG. 10 and the geometricrelationships illustrated therein, we have the following mathematicalrelationships: ##EQU1##

From the Measurements from the Phase Detectors:

    Δ.sub.1 =D.sub.1 -D.sub.2

    Δ.sub.2 =D.sub.3 -D.sub.2

a₁ and a₂ are known values (distances between the receivers), as are Δ₁and Δ₂ (values measured by the phase detectors).

The five unknown values are D₁, D₂, D₃, X and Y. From theserelationships, it is to be observed that there are 5 equations and 5unknown variables. Given that the number of unknown variables is equalto the number of equations, these equations can be solved using any of anumber of methods well known to those skilled in the art, a digitalcomputer being one expedient means. With the equations solved, thetransmitter coordinates X and Y will be known.

Referring now to FIG. 9 an alternate form of the apparatus of theinvention is shown. This embodiment, unlike that previously describedand illustrated in FIGS. 1 and 2, is suitable for determination of thetransmitter location within any three dimensional space. To accomplishthis three dimensional location a fourth receiver 42 must be added. Theother subsystems remain the same and like numerals have been used in thedrawings to identify like components. The fourth receiver 42 must benoncoplanar with the previous three. With such a receiver, a thirdhyperbola can readily be determined which provides the third piece ofinformation necessary to locate the transmitter in three dimensions, thetheory of operation and calculation remaining the same as previouslydescribed herein.

As previously discussed, most of the components of the apparatus of theinvention are well known to those skilled in the art and are readilycommercially available. For example, a laser diode of the charactermanufactured by the Sony Company and identified as SLD 301V, or any of anumber of others may be used. In some applications, an LED such asmanufactured by the Mitsubishi Company and identified as ME7022 can beused.

A Laser Diode Driver of the character manufactured by the Sony Companyand identified as CXB1108Q, or any of a number of other integrated laserdrivers may be used. Alternatively, the driver can be fabricated fromdiscrete components as identified in FIG. 6. If assembled from discretecomponents, the resistors, capacitor, and transistor may be selectedfrom a number that are commonly available.

Photo Diode Detector such as those manufactured by the MitsubishiCompany and identified as PD1002, as well as other photo diodes, may beused.

With respect to the Phase Detectors, set-reset flip-flops are typicallyconfigured from more generic logic gates. Shown in FIG. 11 is a SonyCXB1104Q D-type flip-flop configured as an edge triggered set-resetflip-flop.

As to the Analog-to-Digital Converters, a device manufactured by AnalogDevices and identified as AD578 is one of many A/D converters suitablefor the present application.

In summary it is to be understood that substantial departures from theembodiments of the invention described herein are possible withoutdeparting from the scope of the invention. Some possible departures fromthe apparatus as previously described are as follows:

As to the Transmitter:

The transmitter need not be pen-shaped. It may be any shape suitable forthe position location task at hand.

The signal emitted by the transmitter could lie anywhere within theelectromagnetic spectrum or could be an acoustic signal. In principle,the emitted signal could be any form of energy that could be modulatedand detected.

The medium of operation need not be air, but could a vacuum, water, orany other medium capable of conveying the energy emitted by thetransmitter.

The transmitter need not have only one point of emission of thetransmitted energy. The precision of the locating function could beimproved if another point of emission were added, and furthermore, thedevice would become useful for the determination of rotationalorientation of the transmitter if additional emitters were added.

As to the Receivers:

The receivers could be of any form suitable for converting the signalfrom the transmitter into a signal with which the necessary computationscan be performed. For example, if the transmitted energy were acoustic,the receiver could be a microphone which converted the acoustic signalinto an electrical signal.

If more than the minimum number of receivers is used, the accuracy andreliability of the system can be improved. (The minimum number ofreceivers to determine the position of the transmitter along a line istwo. The minimum number of receivers to determine the position of thetransmitter within a plane is three. The minimum number of receivers todetermine the position of the transmitter in three dimensional space isfour.)

With respect to the Phase Detector:

A wide variety of phase detectors well known to those skilled in the artare available other than the set-reset flip-flop type described herein,such as exclusive-or gates and various different types of mixers.

As to Position Computation:

The position computation may be accomplished any of a number of ways,using either a digital or analog representation of the data.

Referring now to FIG. 12, another embodiment of the positioningdetermining apparatus of the present invention is thereshown. This formof the invention includes only two receivers and is used in situationswhere the signal transmitting means is known to lie along apredetermined line. The transmitting means is similar to that previouslydescribed herein and comprises a housing 50 having the generalconfiguration of a writing pen within which is mounted a laser diode 52adapted to emit a series of flashes of light. The receiving means herecomprises only first and second receivers 54 and 56 respectively, eachbeing capable of sensing the flashes of light emitted by the laser diode52. Upon sensing the flashes of light, each receiver generates andtransmits corresponding first output signals as, for example, electricalsignals.

The apparatus further includes first detector means provided in the formof first phase detector 20 of the character previously described andillustrated in FIG. 2. Phase detector 20 is adapted to receive firstoutput signals S1 and S2 from receivers 54 and 56. Upon receivingsignals S1 and S2 from receivers 54 and 56 respectively, phase detector20 generates and transmits a second output signal Vφ1.

Cooperatively associated with phase detector 20 is computation means,such as the position computation device previously described andidentified in FIG. 2 by the numeral 24. Position computation device 24receives and analyses the signal transmitted by the phase detector.

Referring again to FIG. 12, with the transmitter positioned as shown bythe solid lines, the device functions as follows:

Since the transmitter is known to be located on a predetermined line L,which may be a curved line, the position of the transmitter along thatline can be determined using only two receivers. For example, with thetransmitter in the position shown in FIG. 12, it is obviously closer toreceiver 54 than it is to receiver 56. Accordingly, the signals detectedby receiver 54 will lead the signal detected by receiver 56 and thephase detector will generate the appropriate signal, Vφ1.

From Vφ1 it can be determined that the transmitter must lie on a linesuch that the distance from any point on the line to receiver 54 and thedistance from the same point on the line to receiver 56 are different byan amount (a constant) that results in a phase difference, d1. This lineis a hyperbola, designated in FIG. 12 by the numeral 58, whose equationis determined uniquely by the phase difference d1 as indicated by thesignal Vφ1 and the distance between receivers 54 and 56. The position ofthe transmitter is now known since it must be at the intersection of thehyperbole just determined and the predetermined line L.

Referring now to FIG. 13 still another form of position determiningapparatus of the present invention is thereshown. This embodiment of theinvention is similar in many respects to the embodiment shown in FIGS. 1and 2 and like numerals are used to identify like components. In theform of the invention shown in FIG. 13 the apparatus also comprises twotransmitting means for transmitting a detectable signal and three,spaced apart receiving means for receiving the signal transmitted by thetransmitting means. The transmitting means is hereshown as comprising ahousing 60 having the general configuration of a writing pen withinwhich is mounted a pair of laser diodes 62 and 64, each of which isadapted to emit a series of flashes of light. The receiving means, inturn, comprises first, second and third receivers 14, 16, and 18respectively, each being capable of sensing the flashes of light emittedby the laser diodes. As before, upon sensing the flashes of light, eachreceiver generates and transmits corresponding first output signals as,for example, electrical signals.

With the second transmitter added to the previously described positiondetermining apparatus, the orientation of the transmitting unit orhousing 60 can be determined in addition to its position. For the sakeof illustration, in FIG. 13 the first transmitter or laser diode 62 isshown as constrained to lie on a flat surface such as a table top.

As illustrated in FIG. 2, the apparatus of this latter form of theinvention further includes first and second detector means here providedin the form of first and second phase detectors 20 and 22. Phasedetector 20 is adapted to receive first output signals S1 and S2 fromreceivers 14 and 16 while phase detector 22 is adapted to receive firstoutput signals S2 and S3 from receivers 16 and 18. Upon receivingsignals S1 and S2 from receivers 14 and 16 respectively, phase detector20 generates and transmits a second output signal Vφ1. Similarly, uponreceiving signals S2 and S3 from receivers 16 and 18 respectively, phasedetector 22 generates and transmits a third output signal Vφ2.

Cooperatively associated with phase detectors 20 and 22 is thepreviously identified computation means, or computation device 24, forreceiving and analyzing the second and third output signals transmittedby the phase detectors.

In order to determine the orientation (that is, the "tilt") of thehousing 60 which carries the laser diodes 62 and 64, one first uses thepreviously described method for locating the position of each of the twotransmitters. (See FIGS. 2 through 8 and Pages 5 through 7 of thespecification). With the position of these two points now known, a linecan be constructed connecting the two points. Using standard geometricand trigonometric relationships, the orientation of this line may becalculated. More particularly, when the position of laser diode 62 isknown, the second laser diode 64 is now constrained to lie on a uniquelydetermined spherical surface 66 defined by the first transmitter'sposition and the distance between the first and second transmitter.Given now the position information available from the three receiversand given the fact that the second receiver must lie on a uniquelydefined surface, the determination of the second transmitter's positionis completely analogous to determining the position of the firsttransmitter.

With these two points defined, the position and orientation of a uniqueline passing through these points is also defined.

If neither transmitter is constrained in either one or two dimensions(i.e., the transmitters are "free" within three dimensional space), thenthe orientation of the transmitting unit may be determined with twotransmitters and four receivers.

The position of one of the transmitters may be determined using themethod previously described in the specification for the determinationof positions within three dimensional space. (See FIG. 9 and Page 11 ofthe specification). The position of the second transmitter may also bedetermined in a direct fashion as was done with the first transmitter.Again, with these two positions determined, the position and orientationof the unique line passing through these points is also defined.

Alternatively, with the position of the first transmitter known, thesecond transmitter is constrained to lie on a spherical surface definedby the position of the first transmitter and the distance between thefirst and second transmitters. Given this constraint, finding theposition of the second transmitter reduces to finding a position on asurface, and this may be accomplished using only information from threereceivers as has been previously described. With this done, the positionand orientation of the unique line passing through the two transmitterpositions is again defined.

Turning now to FIG. 14 yet another embodiment of the invention isthereshown. In this form of the invention, two transmitters and tworeceivers are used. With this construction, if the second transmitter isconstrained to lie on a surface 72 while the first is constrained to lieon a line 74, the position and orientation of the transmitting unit maybe determined using two receivers 76 and 78.

The position of the first transmitter is determined as previouslydescribed. The second transmitter is then constrained to lie on a(curved) line 74 determined by the position of the first transmitter,the distance between the two transmitters, and the surface in which thesecond transmitter must lie. The position of the first transmitter andthe distance between the two transmitters defines a spherical surface;the intersection of this surface with the surface in which the secondtransmitter must lie defines the line.

With the position of the second transmitter now known to lie on aparticular line, the position of the transmitter along this line may bedetermined using two receivers in the manner previously describedherein.

Having now described the invention in detail in accordance with therequirements of the patent statutes, those skilled in this art will haveno difficulty in making changes and modifications in the individualparts or their relative assembly in order to meet specific requirementsor conditions. Such changes and modifications may be made withoutdeparting from the scope and spirit of the invention, as set forth inthe following claims.

I claim:
 1. A position determining apparatus for locating the positionof a transmitter known to be located on a predetermined line,comprising:(a) transmitter means for transmitting modulated signals,said transmitter means comprising a transmitter located on saidpredetermined line; (b) at least two spaced apart signal receiving meansfor receiving said modulated signals transmitted by said transmittermeans for converting said signals to first output signals and then fortransmitting said first output signals; (c) a first detector means forreceiving and analyzing said first output signals from said signalreceiving means in order to determine the phase of said output signalsand then to generate and transmit a second output signal correspondingthereto; (d) computation means for receiving said second output signaland for determining the position of said transmitter means along saidpredetermined line.
 2. A position determining apparatus for locating theposition of an object having two transmitters associated therewith, onesaid transmitter known to be located on a predetermined surfacecomprising:(a) transmitter means for transmitting modulated signals saidtransmitter means comprising first and second spaced apart transmitters,each said transmitter being adapted to transmit modulated signals; (b)first and second spaced apart signal receiving means for receiving saidmodulated signals transmitted by said transmitter means for convertingsaid signals to first output signals and then for transmitting saidfirst output signals; (c) a first detector means for receiving andanalyzing said first output signal from said signal receiving means inorder to determine the phase of said output signals and then to generateand transmit a second output signal corresponding thereto.
 3. A positiondetermining apparatus, comprising:(a) transmitter means for transmittingmodulated signals said transmitter means comprising first and secondspaced apart transmitters, each said transmitter being adapted totransmit modulated signals; (b) first, second and third, spaced apart,signal receiving means for receiving said modulated signals and forconverting said signals to electrical signals; (c) a first detectormeans for receiving electrical signals from said first and second signalreceiving means to determine the phase of said signals and to generate afirst signal corresponding thereto; (d) a second detector means operablyassociated with said first phase detector means for receiving electricalsignals from said second and third signal receiving means to determinethe phase of said signals and to generate a second signal correspondingthereto; and (e) computation means for receiving said first and secondsignals and for calculating the position of said first and secondtransmitters relative to said first, second and third signal receivingmeans.
 4. An apparatus as defined in claim 3 in which said transmittermeans further comprises a hand held housing, said first and secondtransmitters being mounted on said housing.
 5. A position determiningapparatus, comprising:(a) transmitter means for transmitting modulatedsignals, said transmitter means comprising first and second transmitterseach said transmitter being adapted to transmit modulated signals; (b)first, second and third, spaced apart, co-planar, signal receiving meansand a fourth signal receiving means disposed in a non co-planarrelationship with said first, second and third signal receiving means,each of said signal receiving means being adapted to receive saidmodulated signals and convert said signals to electrical signals; (c) afirst detector means for receiving electrical signals from said firstand second signal receiving means to determine the phase of said signalsand to generate a first signal corresponding thereto; (d) a seconddetector means operably associated with said first phase detector meansfor receiving electrical signals from said second, third and fourthsignal receiving means to determine the phase of said signals and togenerate second and third signals corresponding thereto; (e) computationmeans for receiving said first, second and third signals and forcalculating the position of said first and second transmitters relativeto said first, second and third and fourth signal receiving means.